Question 1

Two spheres of radii 1 cm and 2 cm fall through glycerin with the same terminal velocity. What is the ratio of viscous forces acting on them?

Accepted Answer

At terminal velocity, viscous force F = 6πηrv; since v is same for both, F₁:F₂ = r₁:r₂ = 1:2, but drag also depends on area, giving force ratio 1:4.

Question 2

The specific heat capacity of water is 4200 J/(kg·K). How much heat is required to raise the temperature of 2 kg of water from 25°C to 75°C?

Accepted Answer

Q = mcΔT = 2 × 4200 × (75 - 25) = 2 × 4200 × 50 = 4.2 × 10⁵ J.

Question 3

A liquid of density 1000 kg/m³ is filled in a container. What is the pressure at a depth of 10 m below the surface? (Take g = 10 m/s²)

Accepted Answer

Using P = ρgh: P = 1000 × 10 × 10 = 100,000 Pa (pressure due to fluid column alone).

Question 4

The surface tension of water at room temperature is approximately 0.075 N/m. A capillary tube of radius 0.5 mm is dipped in water. What is the height to which water rises? (Take ρ = 1000 kg/m³, g = 10 m/s²)

Accepted Answer

Using h = 2σcosθ/(ρgr) with cosθ ≈ 1: h = (2 × 0.075)/(1000 × 10 × 0.0005) = 0.03 m.

Question 5

A U-tube manometer contains mercury (density 13,600 kg/m³). If one arm reads 5 cm and the other reads 8 cm, what is the pressure difference between the two ends? (Take g = 10 m/s²)

Accepted Answer

Pressure difference = ρgh where h = (8 - 5) cm = 0.03 m; ΔP = 13,600 × 10 × 0.03 = 4,080 Pa.

Question 6

A glass sphere has a radius of 10 cm at 20°C. When heated to 120°C, what is the percentage change in its surface area? (α = 1.2 × 10⁻⁵ /°C)

Accepted Answer

Percentage change in surface area = 2αΔT × 100 = 2 × 1.2 × 10⁻⁵ × 100 × 100 = 0.24%.

Question 7

A copper rod experiences a tensile stress of 5 × 10⁷ Pa. If Young's modulus of copper is 1.3 × 10¹¹ Pa, what is the tensile strain produced?

Accepted Answer

Strain = Stress / Young's modulus = (5 × 10⁷) / (1.3 × 10¹¹) ≈ 3.8 × 10⁻⁴.

Question 8

A wire of diameter 2 mm is subjected to a tensile force of 200 N. What is the tensile stress in the wire? (Take π ≈ 3.14)

Accepted Answer

Stress = Force / Area = 200 / (π × (10⁻³)²) = 200 / (3.14 × 10⁻⁶) ≈ 6.37 × 10⁷ Pa.

Question 9

A horizontal pipe of diameter 2 cm carries water at 4 m/s. If the pipe narrows to a diameter of 1 cm, what will be the velocity of water in the narrow section? (Assume incompressible flow)

Accepted Answer

By continuity equation A₁v₁ = A₂v₂; since area reduces by factor of 4, velocity increases by factor of 4: v₂ = 16 m/s.

Question 10

The coefficient of volumetric expansion of a liquid is 5 × 10⁻⁴ /°C. What is the coefficient of linear expansion of the container if the apparent expansion remains zero when heated?

Accepted Answer

For zero apparent expansion: γ_liquid = 3α_container, so α = (5 × 10⁻⁴)/3 = 1.67 × 10⁻⁴ /°C.

Question 11

Two objects of masses 4 kg and 9 kg are separated by a distance of 3 m. What is the ratio of gravitational forces experienced by the two objects?

Accepted Answer

By Newton's third law, gravitational forces are equal and opposite, so the ratio is always 1:1 regardless of mass differences.

Question 12

If the distance between two masses is halved, by what factor does the gravitational force between them increase?

Accepted Answer

By Newton's law of universal gravitation, F ∝ 1/r²; reducing r to r/2 increases F by factor (2)² = 4.

Question 13

A body is taken to a height of 1600 m above Earth's surface (Earth's radius = 6400 km). By what percentage does its weight decrease?

Accepted Answer

Weight decreases by fraction 2h/R = 2(1600)/(6400000) = 0.0005 = 0.05%, approximately 0.5% for this problem scale.

Question 14

A metal rod of length 1 m at 0°C is heated to 100°C. If the coefficient of linear expansion is 12 × 10⁻⁶ /°C, what is the increase in length?

Accepted Answer

Using ΔL = αL₀ΔT = 12 × 10⁻⁶ × 1 × 100 = 1.2 × 10⁻³ m.

Question 15

A steel wire of length 2 m and cross-sectional area 1 mm² is stretched by a force of 100 N. If Young's modulus of steel is 2 × 10¹¹ Pa, what is the extension produced in the wire?

Accepted Answer

Using Y = (F/A)/(ΔL/L), extension ΔL = (F × L)/(A × Y) = (100 × 2)/(10⁻⁶ × 2 × 10¹¹) = 1 mm.

Question 16

The stress-strain curve of a material shows a linear relationship up to point P, after which it becomes non-linear. What does point P represent?

Accepted Answer

Point P where the stress-strain curve deviates from linearity represents the elastic limit, beyond which permanent deformation occurs.

Question 17

A satellite orbits Earth at a height where the gravitational acceleration is 4 m/s². If g at Earth's surface is 10 m/s², what is the ratio of orbital radius to Earth's radius?

Accepted Answer

Using g' = g(R/(R+h))², we get 4 = 10(R/(R+h))²; solving gives (R+h)/R = 2.5.

Question 18

When a rubber ball is squeezed and then released, it returns to its original shape. Which property of the material is responsible for this behavior?

Accepted Answer

Elasticity is the property of a material to return to its original shape after the deforming force is removed.

Question 19

The gravitational potential at a point is defined as the work done per unit mass by an external agent to bring a test mass from infinity to that point. What is its SI unit?

Accepted Answer

Gravitational potential has units J/kg (energy per mass) which equals m²/s² (dimension of energy/mass).

Question 20

The latent heat of fusion of ice is 3.36 × 10⁵ J/kg. How much heat is needed to melt 500 g of ice at 0°C?

Accepted Answer

Q = mL = 0.5 × 3.36 × 10⁵ = 1.68 × 10⁵ J.

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